Question

1. Find the mean of the following data.
(a) 9, 7, 11, 13, 2, 4, 5, 5
(b) 16, 18, 19, 21, 23, 23, 27, 29, 29, 35
(c) 2.2, 10.2, 14.7, 5.9, 4.9, 11.1, 10.5
2. The mean of 8, 11, 6, 14, x and 13 is 66. Find the value of the observation x.
3. The mean of 6, 8, x + 2, 10, 2x - 1, and 2 is 9. Find the value of x and also the value of the
observation in the data.
4. The set of scores 12, 5, 7, -8, x, 10 has a mean of 5. Find the value of x.
5. Find the mean of the following set of integers.
8, 11, –6, 22, –3

Answer 1

1. a) 9, 7, 11, 13, 2, 4, 5, 5

We have to find the mean of the given data.

Solution:

We know that:

Mean = $\dfrac{Sum of all observation}{Total number of observations}$

∴ Mean = $\dfrac{9+7+11+13+2+4+5+5}{8}$

             = $\dfrac{56}{8}$ = 7

Thus, the mean of the given data is 7.

1. b) 16, 18, 19, 21, 23, 23, 27, 29, 29, 35

We have to find the mean of the given data.

Solution:

We know that:

Mean = $\dfrac{Sum of all observation}{Total number of observations}$

∴ Mean = $\dfrac{16+18+19+21+23+23+27+29+29+35}{10}$

             = $\dfrac{240}{10}$ = 24

Thus, the mean of the given data is 24.

1. c) 2.2, 10.2, 14.7, 5.9, 4.9, 11.1, 10.5

We have to find the mean of the given data.

Solution:

We know that:

Mean = $\dfrac{Sum of all observation}{Total number of observations}$

∴ Mean = $\dfrac{2.2+10.2+14.7+5.9+4.9+11.1+10.5}{7}$

             = $\dfrac{59.5}{7}$ = 8.5

Thus, the mean of the given data is 8.5.

2. The mean of 8, 11, 6, 14, x and 13 is 66. Find the value of the observation x

We have to find, the value of x in the given observations.

Solution:

We know that:

Mean = $\dfrac{Sum of all observation}{Total number of observations}$

∴  $\dfrac{8+11+6+14+x+13}{6}$ = 66

⇒ 52 + x = 396

⇒ x = 396 - 52

⇒ x = 344  

Thus, the value of x is 344.        

3. The mean of 6, 8, x + 2, 10, 2x - 1, and 2 is 9. Find the value of x and also the value of the  observation in the data.

We have to find, the value of x and also find the value of observations in the data.

Solution:

We know that:

Mean = $\dfrac{Sum of all observation}{Total number of observations}$

∴  $\dfrac{6+8+(x+2)+10+(2x-1)+2}{6}$ = 9

⇒ 27 + 3x = 54

⇒ 3x = 27

⇒ x = 9

Thus, the value of x is 9.    

The value of the  observation in the data:

6, 8, (9 + 2), 10, (18 - 1) and 2

= 6, 8, 11, 10, 17 and 2

∴ The value of the  observation in the data are 6, 8, 11, 10, 17 and 2.

4. The set of scores 12, 5, 7, -8, x, 10 has a mean of 5. Find the value of x.

We have to find, the value of x in the given observations.

Solution:

We know that:

Mean = $\dfrac{Sum of all observation}{Total number of observations}$

∴ $\dfrac{12+5+7-8+x+10}{6}$  = 5

⇒ 26 + x = 30

⇒ x = 30 - 26

⇒ x = 4  

Thus, the value of x is 4.        

5. Find the mean of the following set of integers.

8, 11, – 6, 22, – 3

We have to find the mean of the given data.

Solution:

We know that:

Mean = $\dfrac{Sum of all observation}{Total number of observations}$

∴ Mean = $\dfrac{8+11-6+22-3}{5}$

             = $\dfrac{32}{5}$ = 6.4

Thus, the mean of the given data is 6.4.

Answer 2

Given:

The mean of the observation is given by the sum of all observations divided by the total number of observations.    

To Find:

We have to find the following

1. Mean of the observation  9, 7, 11, 13, 2, 4, 5, 5 ; 16, 18, 19, 21,23, 23, 27, 29, 29, 35 and 2·2, 10·2, 14·7, 5·9, 4·9, 11·1, 10·5
2. Value of x, where the mean of 8, 11, 6, 14, x, 13 is 66
3. Value of x and the value of the observation in the data, where the mean of 6, 8, x+2, 10, 2x-1, 2 is 9.
4. Value of x, where the mean of 12, 5, 7, -8, x, 10 is 5
5. Mean of the observation 8, 11, -6, 22, -3

Solution:

Arithmetic Mean / Average  = $\frac{Sum\,\ of\,\ all\,observations}{Total\,\ number\, of\,\ all\,observations}$

1. a). Mean =   $\eq \frac{9+7+11+13+2+4+5+5}{8}$                                                                      ∴  Mean  = 7                                                                                                   b)  Mean =   $\eq \frac{16+18+19+21+23+23+27+29+29+35}{10}$                                                 ∴  Mean = 24

       c) Mean = $\frac{2.2+10.2+14.7+5.9+4.9+11.1+10.5}{7}$                                                                    ∴   Mean = 8·5          

    2.    Sum of all observations = 8+11+6+14+x+13 = 52+x

           Total number of obsevations = 6

           Mean =  66

       ⇒    66 =  $\frac{52+x}{6}$      

                 x = 344          

      ∴ The value of the observation, x= 344

    3.  Sum of all observations = 6+8+x+2+10+2x-1+2 = 27+3x

           Total number of obsevations = 6

           Mean =  9

       ⇒    9 =  $\frac{27+3x}{6}$      

                 x = $\frac{27}{3}$

                 x = 9          

      ∴ The value of the x = 9 and values of observation in the data are 6, 8, 11, 10, 17 and 2.

      4.  Sum of all observations = 12+5+7+-8+x+10 = 26+x

           Total number of obsevations = 6

           Mean =  5

       ⇒    5 =  $\frac{26+x}{6}$      

                 x = 4

       ∴ The value of the observation, x= 4.

    5.  Mean =   $\eq \frac{8+11-6+22-3}{5}$

                    = $\frac{32}{5}$

∴ The mean of the observation = $\frac{32}{5}$ = 6·4